in triangle JLP the meaasure of angle JMP = 3x-6
line JK = 3y - 2 and line JK = 5y - 8.
If line JM is an altitude of triangle JLP find x

Question

in triangle JLP the meaasure of angle JMP = 3x-6
line JK = 3y - 2 and line JK = 5y - 8.
If line JM is an altitude of triangle JLP find x

gunnar · Answer

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directrix · Answer

@gunnar   You have segment JK with two different measures. Is this a typo?

line JK = 3y - 2 and line JK = 5y - 8 ?

gunnar · Answer

Yes it is i ment to say JK is 3y-2 and LK= 5y-8 @Directrix

directrix · Answer

There must be other parts of this problem because the segment lengths have no bearing on the computation of x.

Line JM is an altitude of triangle JLP so that means segment JM is perpendicular to segment LP and <JMP is a right angle. The measure of a right angle is 90.

That gives the equation 3x - 6 =90

@gunnar If 3x - 6 = 90, then what does x = ?

gunnar · Answer

@directrix

gunnar · Answer

@directrix ?

directrix · Answer

If segment PK is a median to side LJ, then JK = KL because a median is a segment drawn from any vertex of a triangle to the midpoint of the opposite side.

JK = KL
5y - 8 = 3y - 2
2y - 8 = -2

@gunnar  Solve for y and then substitute what you get back into the expression for LK.